Landauer–Büttiker and Thouless Conductance

L. Bruneau, V. Jakšić*, Y. Last, C. A. Pillet

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


In the independent electron approximation, the average (energy/charge/entropy) current flowing through a finite sample $${\mathcal{S}}$$S connected to two electronic reservoirs can be computed by scattering theoretic arguments which lead to the famous Landauer–Büttiker formula. Another well known formula has been proposed by Thouless on the basis of a scaling argument. The Thouless formula relates the conductance of the sample to the width of the spectral bands of the infinite crystal obtained by periodic juxtaposition of $${\mathcal{S}}$$S. In this spirit, we define Landauer–Büttiker crystalline currents by extending the Landauer–Büttiker formula to a setup where the sample $${\mathcal{S}}$$S is replaced by a periodic structure whose unit cell is $${\mathcal{S}}$$S. We argue that these crystalline currents are closely related to the Thouless currents. For example, the crystalline heat current is bounded above by the Thouless heat current, and this bound saturates iff the coupling between the reservoirs and the sample is reflectionless. Our analysis leads to a rigorous derivation of the Thouless formula from the first principles of quantum statistical mechanics.

Original languageAmerican English
Pages (from-to)347-366
Number of pages20
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - 1 Aug 2015

Bibliographical note

Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.


Dive into the research topics of 'Landauer–Büttiker and Thouless Conductance'. Together they form a unique fingerprint.

Cite this